I have a Dell Inspiron 580 (i580-6654NBC) core i3 550
I want to upgrade the graphics card that I already have to a evga gtx 780 6gb that I found for a great price
Problem is I don't know if it's compatible or if it will even fit in the case

get the model number off of your motherboard and look it up that way
that model may have two or three different motherboards for that same model
so I would suggest looking it up by the motherboard and not the brand of the computer
and see what the motherboard can handle